This invention relates generally to non-destructive material analysis and characterization systems and methods and, more particularly, relates to optically based materials analysis and characterization systems that employ light pulses of picosecond and sub-picosecond duration to generate a localized stress in a sample that results in propagating strain waves, and that detect changes in optical constants of the sample material due to the propagating strain waves.
A number of U.S. Patents exist in the general area of picosecond ultrasonics. In most of these U.S. Patents a pump light pulse is directed at the surface of a sample. The pump light pulse raises the temperature of a layer near the surface of the sample and sets up a stress in this region. A time-varying strain is then generated in the sample. The strain is detected by means of a probe light pulse applied to the sample at a later time. Hereinafter this approach will be referred to as the xe2x80x9cstandard methodxe2x80x9d. From the arrival time, amplitude, and shape of the detected signals, a data processor is enabled to determine a number of characteristics of the sample. These characteristics include, but are not limited to, the film thickness, the adhesion between a film and the substrate, the adhesion between one film and another film, the orientation of crystalline grains making up a film, the size of grains, the crystal phase of a film, the electrical resistivity of a film, the rate of electromigration within a film, and the yield stress of a film.
In some of these U.S. Patents measurements can be made by means of a second method, referred to herein for convenience as a xe2x80x9cgrating methodxe2x80x9d. In this approach, the pump light is divided into two beams that are directed onto the sample surface at oblique angles. Because of the constructive and destructive interference between the two beams, the intensity of the pump light varies periodically across the sample surface. Thus, the temperature rise of the sample surface and the induced stress will also vary periodically across the sample surface. This stress launches a strain disturbance into the sample that varies periodically across the sample surface. This strain field causes the optical constants of the sample, and the displacement of the sample surface, to vary across the sample surface and, as a consequence, when a probe pulse is incident onto the surface a fraction of the probe pulse will be diffracted, rather than undergoing specular reflection. Thus, the strain field acts as a diffraction grating. By a measurement of the intensity of the diffracted probe light as a function of the time after the application of the pump light pulse, the propagation of strain in the sample can be investigated, and physical properties of the sample determined. The grating method can also be used to determine the various sample properties that were listed above.
These two methods each have some limitations. For example, in the standard method, in order to determine the thickness of a film the sound velocity in the film must be known. This value can be taken from measurements made on a bulk sample of the same material composition as the film. In some cases, it is also possible to estimate the sound velocity from a measurement of the reflection coefficient of the strain pulse at the interface between one film and another. This measurement enables a comparison of the acoustic impedances of the two films to be made.
The grating method also exhibits a number of limitations. For example, it is necessary to build the apparatus in a way that ensures that the phase relation between the two pump beams remains constant. In addition, the diffracted component of the probe light may have a low intensity and thus may be difficult to measure accurately in the presence of light diffusely scattered from the surface of the sample.
Based on the foregoing, it can be appreciated that a need exists to provide an improved approach to ultrasonic sample characterization that overcomes the foregoing and other problems.
It is a first object and advantage of these teachings to provide an improved sample characterization system and method that overcomes the foregoing an other problems.
It is another object and advantage of these teachings to provide an improved sample characterization system and method that employs an optical mask.
The foregoing and other problems are overcome and the objects of the invention are realized by methods and apparatus in accordance with embodiments of this invention.
An improved method and apparatus in accordance with these teachings generates and detects strain pulses in a sample, while retaining many of the advantages of the standard method, while at the same time making it possible to determine the sound velocity in the sample. A transparent plate, referred to herein for convenience as a mask, is placed over the sample. The bottom of the plate has a periodic grating etched into its surface. A pump light pulse is directed through the transparent mask onto the sample. The periodic grating of the mask distorts the wavefront of the light pulse and, as a result, the intensity of the light incident onto the film varies periodically with position across the sample surface. This results in a heating of the film surface that varies periodically with position. The regions of the film that are heated expand and, as a result, spatially distributed strain pulses (disturbances) are launched into the sample. The strain pulses result in a change in the optical constants of the sample, and this change is detected by means of a time-delayed probe pulse also directed onto the sample through the transparent mask. As in the standard method and the grating method, the improved method in accordance with the teachings herein can be used to determine various characteristics of the sample. These characteristics include, but need not be limited to, the film thickness, the adhesion between a film and the substrate, the adhesion between one film and another film, the orientation of crystalline grains making up a film, the size of grains, the crystal phase of a film, the electrical resistivity of a film, the rate of electromigration within a film, and the yield stress of a film.
In one preferred embodiment, the pump and probe beams are directed through the mask at normal incidence. The probe is delayed relative to the pump by means of a variable optical path provided by a movable stage. The change in the intensity of the reflected probe beam is measured as a function of the time delay between the application of the pump and probe pulses. To improve the signal to noise ratio the intensity of the pulses composing the pump beam is modulated at frequency f by means of an acousto-optic modulator. The output of the detector of the reflected probe beam is fed into a lock-in amplifier for which the reference signal is at the same frequency f. The measured change xcex94R(t) in reflectivity of the sample is compared with the results of a simulated reflectivity change xcex94Rsim(t). The change xcex94Rsim(t) can be determined as follows: A) An initial estimate is made for the parameters of the sample. These parameters include, but are not necessarily limited to, the thickness, density, sound velocity, thermal expansion, specific heat, and optical constants of the different films, the adhesion between the films, the orientation of crystalline grains making up a film, the size of grains, the crystal phase and electrical resistivity of each film. B) Based on these assumed values, the stress in the structure that is induced by the pump light pulse is calculated. C) The time-dependent strain in the sample is then calculated. D) From this strain, the expected change in reflectivity xcex94Rsim(t) is found. E) This change is compared with the measured reflectivity xcex94R(t). The parameters of the sample are then adjusted and the procedure repeated in order to achieve the best possible agreement between xcex94R(t) and xcex94Rsim(t).
A method and a system are thus disclosed for determining at least one characteristic of a sample containing a substrate and at least one film disposed on or over a surface of the substrate. The method includes a first step of placing a mask over a free surface of the at least one film, where the mask has a top surface and a bottom surface that is placed adjacent to the free surface of the film. The bottom surface of the mask has formed therein or thereon a plurality of features for forming at least one grating. A next step directs optical pump pulses through the mask to the free surface of the film, where individual ones of the pump pulses are followed by at least one optical probe pulse.
In accordance with an aspect of these teachings the pump pulses are spatially distributed by the grating for launching a plurality of spatially distributed, time varying strain pulses within the film. The strain pulses cause a detectable change in optical constants of the film.
A next step detects a reflected or a transmitted portion of the probe pulses, which are also spatially distributed by the grating.
A next step of the method measures a change in at least one characteristic of at least one of reflected or transmitted probe pulses due to the change in optical constants, and a further step determines the at least one characteristic of the sample from the measured change in the at least one characteristic of the probe pulses.
In addition to changes in reflectivity arising from the strain pulses that are launched in the sample, there may be components that arise from a spatial variation in temperature, and/or from a spatial variation in a density of electrons and holes in the sample.
For example, the sample may include at least one region that is implanted during an ion implant process and, using the spatially varying density of electrons and holes in the film, a determined characteristic of the sample can be related to at least one of (A) a number of ions implanted per unit area of the surface of the sample; (B) a kinetic energy of the ions that are directed at the surface of the sample; (C) a direction at which the ion beam is incident onto the surface of the sample; (D) an ion current per unit area during the ion implant process; (E) the species of the implanted ion; (F) the charge on the implanted ion; (G) a duration of time that the ion-implanted sample is annealed; and (H) a temperature at which the ion-implanted sample is annealed.
An optical mask is also disclosed herein, and forms a part of these teachings.
Also disclosed is a method for determining the electrical resistivity of a film that comprises part of a sample having an underlying substrate. The method includes steps of: (A) placing a mask over a free surface of the film, the mask having a top surface and a bottom surface that is placed adjacent to the free surface of the film, the bottom surface of the mask comprising a plurality of features having a known feature repeat distance w; (B) directing optical pump pulses through the mask to the free surface of the film, individual ones of the pump pulses being followed by at least one optical probe pulse, said pump pulses being spatially distributed by said at least one grating for generating a spatially distributed temperature variation within the film that causes a change in optical constants of the film; (C) detecting a reflected or transmitted portion of said probe pulses, said probe pulses also being spatially distributed by said at least one grating; (D) measuring xcex94R(t) as a function of the time t after the application of the pump pulses using the mask of known repeat distance w; (E) assuming values for the thermal conductivity xcexafilm of the film, the thermal conductivity xcexasub of the substrate, and the Kapitza conductance "sgr"K between the film and the substrate; (F) calculating an initial temperature distribution within the film; (G) calculating the temperature distribution within the film at later times based on the assumed values for the thermal conductivity of the film, the thermal conductivity of the substrate, and the Kapitza conductance between the film and the substrate; (H) calculating an expected change in reflectivity xcex94R(t) based on the calculated temperature distribution; (I) adjusting the parameters xcexafilm, xcexasub, and "sgr"K, and repeating Steps (F)-(H) so as to obtain a best fit to the measured xcex94R(t); and calculating the electrical resistivity from the thermal conductivity.